PREHEAT the oven to 400°F.
HEAT 1 tablespoon of the olive oil in a large skillet over medium-high heat.
ADD the mushrooms and cook, stirring occasionally, until lightly browned, about 3 minutes.
ADD 1/2 cup of the onion and the bell pepper.
COOK, stirring occasionally, until the onion is tender, 3 minutes.
ADD half the garlic and the oregano.
COOK, stirring, for 1 minute more.
REMOVE from the heat and stir in 1/2 cup of the basil, the almond flour, lemon zest, and 1/2 teaspoon of the salt.
TRANSFER the mushroom mixture to a bowl and set aside to cool slightly.
RINSE and dry the skillet.
TRIM away any excess fat from the edges of the steak.
PLACE the steak on a work surface.
With the notched edge of a meat mallet, POUND the steak to about 1/4 inch thick.
SPREAD the mushroom mixture over the steak to within 1/2 inch of the edges.
Starting on a long side, ROLL up the meat and tie it with 100% cotton kitchen string.
In a medium bowl, COMBINE the green beans, 2 tablespoons of the oil, the remaining garlic, and the remaining 1/2 teaspoon salt and toss.
SPREAD the beans evenly on a large baking sheet. Roast for 18 to 20 minutes, until the beans are lightly browned and crisp-tender.
In the same skillet, HEAT the remaining 2 tablespoons olive oil over medium-high heat.
SEAR the meat in the hot oil and cook, turning occasionally, to sear evenly on all sides.
REMOVE the meat from the skillet.
ADD the remaining 1/2 cup onion to the skillet.
COOK, stirring, until softened, about 5 minutes
STIR in the tomato paste, then whisk in the broth.
BRING the broth to a boil.
RETURN the meat to the skillet and spoon some of the sauce over the meat.
COVER and reduce the heat to medium-low.
SIMMER gently, turning once, until the internal temperature of the roulade is 160°F, 8 to 10 minutes.
SPRINKLE with the remaining 1/4 cup basil.
TRANSFER the roulade to a cutting board and let rest for 5 to 10 minutes.
REMOVE the string and cut into 1/2-inch-thick slices.
SERVE the meat and sauce with the green beans.